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Question: Suppose that two players, Bob and John, play the following matrix game.
Part a: Find all of the game's pure-strategy Nash equilibria. Now suppose that the players play this game twice in a row. They observe what each other did in the first stage before they decide what to do in the second stage. Each player's payoff is the (undiscounted) sum of his payoffs in the first and second stages.
Part b: Find all Subgame Nash Equilibria of this finitely repeated game.
Part c: Why may it be possible to support non-equilibrium outcomes in a stage game when the game is repeated a finite number of times.
Part d: Why might it be possible to support cooperation in an infinitely-repeated
A problem with an exercise about Cournot game. It is very complex and it is composed by different question and it is impossible for me to write the complete text.
Construct a belief space in which the described situation is represented by a state of the world and indicate that state.
A manufacturer of a new, less expensive type of light bulb claims that this product is very well made and even more reliable than the higher priced competitive light bulbs.
Compute the Nash equilibria and subgame perfect equilibria for the following games. - Do so by writing the normal-form matrices for each game and its subgames.
Draw this game in extensive form. - Using a matrix representation, find all the pure-strategy Bayesian Nash equilibria for this game.
Samples of our students from an applied experimental design class were polled regarding the number of hours they spent studying for the last exam. All students anonymously submitted the number of hours on a 3x5 card.
Specify this situation as a strategic game. - Use the symmetry of the game to show that the unique equilibrium payoff of each player is 0.
Prove or disprove: Every finite belief space has a consistent belief subspace.- Prove or disprove: If Y˜ i(ω) is inconsistent for some player i ∈ N, then Y˜ (ω) is also inconsistent.
Determine whether this game has a symmetric mixed-strategy Nash equilibrium in which each player selects X with probability p. If you can find such an equilibrium, what is p?
Assume that there are at least two non owners, both of whose values of a horse exceed σ1. Find the core of this game.
Suppose that the set of policies is one-dimensional and that each player's preferences are single-peaked. - Find the core of the q-rule game for any value of q with n/2 ≤ q ≤ n.
If it is true, explain why. If it is false, provide a game that illustrates that it is false. "If a Nash equilibrium is not strict, then it is not efficient."
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